My thinking was that it can't be the Blades, as the courier says it is a 'he' that is sending the letters, so that rules out Delphine. Esburn didn't know there was a current Dragonborn when you meet him, so that rules him out. Not sure who else it would be.

EDIT:

Was just thinking, Arngier? But how would he get a letter out? Anyhoo...

one you spelt sheogorath wrong but it's fine it's a hard word to spell and sheogorath is a dadric prince of maddness so in his letter he would write i'm just talking to a tomato it is a amazing conversacion